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EN
The dynamics of slightly diverging two-dimensional beams whose direction forms a constant angle θ with the equilibrium straight magnetic strength is considered. The approximate dispersion relations and corresponding links which specify hydrodynamic perturbations in confined beams are derived. The study is dedicated to the diffraction of a magnetosonic beam and nonlinear thermal self-action of a beam in a thermoconducting gaseous plasma. It is shown that the divergence of a beam and its thermal self-action is unusual in some particular cases of parallel propagation (θ = 0) and has no analogues in the dynamics of the Newtonian beams. The nonlinear attenuation of Newtonian beams leads to their defocusing in gases, whereas the unusual cases correspond to the focusing in a presence of magnetic field. The examples of numerical calculations of thermal self-action of magnetoacoustic beams with shock fronts are considered in the usual and unusual cases of diffraction concerning stationary and non-stationary self-action. It is discovered that the diffraction is more (θ = 0) or less (θ = π/2) manifested as compared to that of the Newtonian beams. The beams which propagate oblique to the magnetic field do not reveal diffraction. The special case, when the sound and Alfvénic speeds are equal, is discussed. This magnetosonic beams incorporate acoustic and Alfvénic properties and do not undergo diffraction in this particular case.
EN
The nonlinear interaction of magnetoacoustic waves in a plasma is analytically studied. A plasma is an open system. It is affected by the straight constant equilibrium magnetic flux density forming constant angle with the wave vector which varies from 0 till π. The nonlinear instantaneous equation which describes excitation of secondary wave modes in the field of intense magnetoacoustic perturbations is derived by use of projecting. There is a diversity of nonlinear interactions of waves in view of variety of wave modes, which may be slow or fast and may propagate in different directions. The excitation is analysed in the physically meaningful cases, that is: harmonic and impulsive exciter, oppositely or accordingly directed dominant and secondary wave modes.
EN
Nonlinear excitation of the entropy perturbations by magnetosonic waves in a uniform and infinite plasma model is considered. The wave vector of slow or fast mode forms an arbitrary angle θ (0 ≤ θ ≤ π) with the equilibrium straight magnetic field, and all perturbations are functions of the time and longitudinal coordinate. Thermal conduction is the only factor which destroys isentropicity of wave perturbations and causes the nonlinear excitation of the entropy mode. A dynamic equation is derived which describes excitation of perturbation in the entropy mode in the field of dominant magnetosonic mode. Effects associatiated with temperature dependent and anisotropic thermal conduction are considered and discussed.
EN
The self-refraction of some beams in a Newtonian fluid is theoretically studied. Asingle pulse that takes the shape of an isosceles triangle at a transducer and a solitary shockwave are considered as examples. The novelty lies in the consideration of a quasi-stationaryshock wave (with positive or negative pressure) and negative triangular pulses. We concludethat waveforms with negative excess pressure undergo self-focusing, in contrast to those withpositive excess pressure. The difference in self-refraction of quasi-stationary and impulse beamsis revealed by means of numerical modeling.
EN
The diversity of wave modes in the magnetic gas gives rise to a wide variety of nonlinear phenomena associated with these modes. We focus on the planar fast and slow magnetosound waves in the geometry of a flow where the wave vector forms an arbitrary angle θ with the equilibrium straight magnetic field. Nonlinear distortions of a modulated signal in the magnetic gas are considered and compared to that in unmagnetised gas. The case of acoustical activity of a plasma is included into consideration. The resonant three-wave non-collinear interactions are also discussed. The results depend on the degree of non-adiabaticity of a flow, θ, and plasma-β.
EN
The magnetoacoustic heating of plasma by harmonic or periodic saw-tooth perturbations at a transducer is theoretically studied. The planar fast and slow magnetosound waves are considered. The wave vector may form an arbitrary angle θ with the equilibrium straight magnetic field. In view of variable θ and plasma-β, the description of magnetosound perturbations and appropriate magnetosound heating is fairly difficult. The scenario of heating depends not only on plasma-β and θ, but also on a balance between nonlinear attenuation at the shock front and inflow of energy into a system. Under some conditions, the average over the magnetosound period force of heating may tend to a positive or negative limit, tend to zero, or may remain constant when the distance from a transducer tends to infinity. Dynamics of temperature specifying heating differs in thermally stable and unstable cases and occurs unusually in the isentropically unstable flows.
EN
Nonlinear effects of planar and quasi-planar magnetosound perturbations are discussed. Plasma is assumed to be an ideal gas with a finite electrical conductivity permeated by a magnetic field orthogonal to the trajectories of gas particles. The excitation of non-wavemodes in the field of intense magnetoacoustic perturbations,i.e., magnetoacoustic heating and streaming, is discussed. The analysis includes a derivation of instantaneous dynamic equations independent of the spectrum and periodicity of sound.
EN
The nonlinear interaction of wave and non-wave modes in a gas planar flow are considered. Attention is mainly paid to the case when one sound mode is dominant and excites the counter-propagating sound mode and the entropy mode. The modes are determined by links between perturbations of pressure, density, and fluid velocity. This definition follows from the linear conservation equations in the differentia form and thermodynamic equations of state. The leading order system of coupling equations for interacting modes is derived. It consists of diffusion inhomogeneous equations. The main aim of this study is to identify the principle features of the interaction and to establish individual contributions of attenuation (mechanical and thermal attenuation) in the solution to the system.
EN
Excitation of the entropy mode in the field of intense sound, that is, acoustic heating, is theoretically considered in this work. The dynamic equation for an excess density which specifies the entropy mode, has been obtained by means of the method of projections. It takes the form of the diffusion equation with an acoustic driving force which is quadratically nonlinear in the leading order. The diffusion coefficient is proportional to the thermal conduction, and the acoustic force is proportional to the total attenuation. Theoretical description of instantaneous heating allows to take into account aperiodic and impulsie sounds. Acoustic heating in a half-space and in a planar resonator is discussed. The aim of this study is to evaluate acoustic heating and determine the contribution of thermal conduction and mechanical viscosity in different boundary problems. The conclusions are drawn for the Dirichlet and Neumann boundary conditions. The instantaneous dynamic equation for variations in temperature, which specifies the entropy mode, is solved analytically for some types of acoustic exciters. The results show variation in temperature as a function of time and distance from the boundary for different boundary conditions.
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